By default, Full Slate automatically accepts appointments as long as your booking rules are followed. Remember that the only appointments offered to clients are days and times when a provider is available. So as long as you block out times that are unavailable, there shouldn't be any conflicts.
If you prefer, however, you can review each appointment request and decide whether to accept or decline case-by-case basis. When you log in, you'll see the number of appointment requests received on the 'Home' tab, and a list of the specific dates/times pending approval on the 'Schedule' tab. Click to highlight one of these on the calendar and see details of the request.
You can check who requested an appointment, even contact them if you want to screen new clients. Once you've decided what to do, click 'Accept' or 'Decline.' Appointments you accept stay on your calendar; ones you decline disappear. Full Slate can take care of notifying the client on your behalf.
Note: You have the opportunity to accept or decline a class when it is added to your schedule (if 'Class times' are set to 'Chosen by client'), but you will not need to accept (or be able to decline) each individual client that is added to a class.